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Hindsight comments:

• (Section 4) We say “M-matrix” , but really what matters is that it’s (weakly) diagonally dominant, which can be solved in ~O(n logn) via Spielman & Tang 2006. The M-matrix machinery extends these properties to some non-diagonally-dominant matrices, and it’s true that our Laplacian is an M-matrix, but that’s not really needed here.